Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
We derive analytic expressions for the possibility, probability, and expected size of global spread- ing events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed and undirected edges and arbitrary degree-degree correla- tions. Our work extends previous theoretical developments for the undirected case, and we provide numerical support for our findings by investigating an example class of networks for which we are able to obtain closed-form expressions.
Payne, Joshua L.; Harris, Kameron Decker; and Dodds, Peter Sheridan, "Exact Solutions for Social and Biological Contagion Models on Mixed Directed and Undirected, Degree-Correlated Random Networks" (2011). Open Dartmouth: Faculty Open Access Articles. 1989.